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# Calculus 151 Regression Project - PowerPoint PPT Presentation

Calculus 151 Regression Project. Data collected from the NJ Department of Education Website. NJ Standardized Test Scores. 76.8 – 75.2 1.6 Average Rate of Change = 02 - 11 = -9 = - .778. Sine Regression. Instantaneous Rate of Change at 2003 = -5.174.

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### Calculus 151 Regression Project

Data collected from the NJ Department of Education Website

76.8 – 75.2 1.6

Average Rate of Change = 02 - 11 = -9 = - .778

Instantaneous Rate of Change at 2003 = -5.174

Quartic RegressionR2 =.555

Instantaneous Rate of Change at 2003 = -1.826

Limit x 6.5- 75.25657 Limit x 6.5+ 71.669602

Limit x 6.5 73.463086

Limit x - ∞ ∞ Limit x ∞ DNE

Derivatives of exponential, logarithmic, and sine regressions

Y’= 74.56303051 *.9993957215^x *ln(.9993957215)

Y’= -.6345494264

x

Y’=-6.784189065* cos(-2.304469566 x + 1.333706904)

Newton’s Methodfinding zeros of the cubic regression

X0=23.74251964

X0=23.74251964

f’(c) = 75.682- 76.565

11-2

f’(c) = - .883

9

f’(c) = -.098

c = X

f(c) = Y4

f’(c) = Y5

Y= -.098(x – 3.4931) + 71.661

Y= -.098(x – 6.9124) + 75.325

Y= -.098(x – 9.67854) +72.782

The Regression has a minimum at 5.4093854 and a maximum at 10.033224. It is increasing between [5.4093854, 10.033224] ,and is decreasing between (- ∞ , 5.4093854) U (10.033224, ∞).

Second Derivative Zero

Inflection Point

Concave up

Concave down

First Derivative Maximum

Estimate Area is

668.504

72.432

73.684

77.426

74.644

76.352

71.138

76.517

74.42

71.891

Estimate Area is

670.836

76.352

71.138

76.517

74.42

71.891

77.426

72.432

73.684

76.976

11

Area=∫02 2.943926518sin(-2.304469566x+1.333706904) +74.26459702dx

F(x)= 1.277485527cos(-2.304469566x +1.333706904)+74.26459702x

F(11)- F(02)≈ 817.47-147.26≈ 670.21

Area ≈ 670.21

Average Value of Calculus

Area= the sum of the % of students proficient in Mathematics over the past 9 years

Average % of students 670.69193

proficient in Mathematics = 9 ≈ 74.55%

for each year